That is a tough one. Handling Tasks on Stories that do not get completed during Sprints has always been a problem. This has to do with the lack of preferences in Scrum.

The reason for the hiding is to clearly seperate Task estimation (in hours) from Story estimation (in Story Points) and to make a distinction between the Team's domain (Sprint Backlog) and the Product Owner's domain (Product Backlog). Additional concerns exist, e.g. concerning UI cluttering).

Only one contra to think about is, that the Team has to estimate the Stories in the Product Backlog. If a Story is killed from a Sprint (or is not "done" on Sprint end) and lose its priority, then later it will be difficult to estimate the partly finished Stories.
I agree with you, especially the last point (UI ckuttering) is important. I like the minimalist approach of kunagil as a pure Scrum tool.
From my point of view it is possible to close this issue.

I always post a comment on a rejected story which explains why the story was not accepted. This always includes what was completed and what is still missing. This helps a lot when the story needs to be reestimated for a new sprint.

Thanks, that seems to be a practical idea to deal with.